OFFSET
0,5
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
M. H. Albert, M. D. Atkinson and Robert Brignall, The enumeration of three pattern classes, arXiv:1206.3183 [math.CO] (2012), p. 30.
Index entries for linear recurrences with constant coefficients, signature (16,-112,449,-1132,1852,-1952,1264,-448,64).
FORMULA
G.f.: x^4*(2-12*x+24*x^2-8*x^3-41*x^4+57*x^5-16*x^6)/((1-x)*(1-3*x+x^2)*(1-2*x)^6).
MAPLE
A219759 := proc(n)
if n <= 1 then
0;
else
2^n*(881*n^2/24-14393*n/60+137+7*n^4/24-49*n^3/8+n^5/120) -384+ 64*A001906(n+2) ;
%/64 ;
end if;
end proc:
seq(A219759(n), n=0..20) ; # R. J. Mathar, Aug 19 2022
MATHEMATICA
CoefficientList[Series[x^4 (2 - 12 x + 24 x^2 - 8 x^3 - 41 x^4 + 57 x^5 - 16 x^6)/((1 - x) (1 - 3 x + x^2) (1 - 2 x)^6), {x, 0, 28}], x] (* Bruno Berselli, Nov 30 2012 *)
LinearRecurrence[{16, -112, 449, -1132, 1852, -1952, 1264, -448, 64}, {0, 0, 0, 0, 2, 20, 120, 570, 2355, 8841, 30906}, 40] (* Harvey P. Dale, Mar 01 2023 *)
PROG
(Maxima) makelist(coeff(taylor(x^4*(2-12*x+24*x^2-8*x^3-41*x^4+57*x^5-16*x^6)/((1-x)*(1-3*x+x^2)*(1-2*x)^6), x, 0, n), x, n), n, 0, 28); /* Bruno Berselli, Nov 29 2012 */
(Magma) I:=[0, 0, 0, 0, 2, 20, 120, 570, 2355, 8841, 30906, 102187, 323053]; [n le 11 select I[n] else 16*Self(n-1) -112*Self(n-2) + 449*Self(n-3) - 1132*Self(n-4) + 1852*Self(n-5) - 1952*Self(n-6) + 1264*Self(n-7) - 448*Self(n-8) + 64*Self(n-9): n in [1..30]]; // Vincenzo Librandi, Dec 14 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 28 2012
STATUS
approved